Anita Gill recently assumed responsibility for a large investment portfolio.She wonders whether industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks: Using $\alpha$ = .01, the observed chi-square value is ___.
A)24.93
B)8.17
C)32.89
D)6.59
E)4.89

Question

Anita Gill recently assumed responsibility for a large investment portfolio.She wonders whether industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks:  Using $\alpha$ = .01, the observed chi-square value is ___.
A)24.93 
B)8.17 
C)32.89 
D)6.59 
E)4.89

Quizplus · Accepted Answer

To calculate the chi-square value, we can use the formula: 
χ2 = Σ (O-E)2 / E 
where O = observed frequency, E = expected frequency. 
First, we need to calculate the expected frequency for each cell in the contingency table:

Expected frequency = (row total * column total) / sample size

For example, the expected frequency for the cell in the first row and first column is: 
(50 * 70) / 200 = 17.5

Using this formula, we can calculate the expected frequency for all cells and get the following table:

| Manufacturing | Retail | Utilities | Total 
------------------|---------------|--------|-----------|------- 
Aggressive Growth |    17.5       |  35.0  |    17.5   |  70.0 
Growth            |    22.5       |  45.0  |    22.5   |  90.0 
Income            |    10.0       |  20.0  |    10.0   |  40.0 
Total             |    50.0       | 100.0  |    50.0   | 200.0

Next, we can calculate the chi-square value by comparing the observed frequency in each cell with the expected frequency:

χ2 = [(45-22.5)2/22.5] + [(30-35)2/35] + [(25-17.5)2/17.5] + [(35-20)2/20] + [(50-45)2/45] + [(15-10)2/10]

χ2 = 10 + 0.7143 + 3.5714 + 7.5 + 0.5556 + 2.5

χ2 = 25.8413

Using a chi-square distribution table with (3-1)(4-1) = 6 degrees of freedom and a significance level of .01, we find the critical value to be 16.81. Since the observed chi-square value (25.8413) is greater than the critical value (16.81), we reject the null hypothesis and conclude that there is a significant relationship between industry sector and investment objective. The best choice is therefore (C), 32.89, as it is the closest option to the calculated chi-square value.

Anita Gill Recently Assumed Responsibility for a Large Investment Portfolio α\alphaα

Anita Gill Recently Assumed Responsibility for a Large Investment Portfolio $\alpha$